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Articles 361 - 390 of 697
Full-Text Articles in Applied Mathematics
Interactions Of Thermoelastic Beam In Modified Couple Stress Theory, Rajneesh Kumar, Shaloo Devi
Interactions Of Thermoelastic Beam In Modified Couple Stress Theory, Rajneesh Kumar, Shaloo Devi
Applications and Applied Mathematics: An International Journal (AAM)
This paper is concerned with the study of thermoelastic beam in modified couple stress theory. The governing equations of motion for modified couple stress theory and heat conduction equation for non-Fourier (non-classical process) are investigated to model the vibrations in a homogeneous isotropic thin beam in a closed form by employing the Euler Bernoulli beam theory. The generalized theories of thermoelasticity with one and two relaxation times are used to model the problem. Both ends of the beam are simply supported. The Laplace transform technique applied to solve the system of equations which are written in dimensionless form. A general …
Applications Of Planar Newtonian Four-Body Problem To The Central Configurations, M. R. Hassan, M. S. Ullah, Md. Aminul Hassan, Umakant Prasad
Applications Of Planar Newtonian Four-Body Problem To The Central Configurations, M. R. Hassan, M. S. Ullah, Md. Aminul Hassan, Umakant Prasad
Applications and Applied Mathematics: An International Journal (AAM)
The present study deals with the applications of the planar Newtonian four-body problem to
the different central configurations. The basic concept of central configuration is that the
vector force must be in the direction of the position vector so that the origin may be taken at
the centre of mass of the four bodies and the force towards the position vector multiplied by
corresponding inverse mass is directly proportional to the position vector relative to the
centre of mass. For applying the Newtonian four body problem to the central configuration,
the equations of motion of four bodies have been established …
Effective Modified Hybrid Conjugate Gradient Method For Large-Scale Symmetric Nonlinear Equations, Jamilu Sabi'u, Mohammed Y. Waziri
Effective Modified Hybrid Conjugate Gradient Method For Large-Scale Symmetric Nonlinear Equations, Jamilu Sabi'u, Mohammed Y. Waziri
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we proposed hybrid conjugate gradient method using the convex combination of FR and PRP conjugate gradient methods for solving Large-scale symmetric nonlinear equations via Andrei approach with nonmonotone line search. Logical formula for obtaining the convex parameter using Newton and our proposed directions was also proposed. Under appropriate conditions global convergence was established. Reported numerical results show that the proposed method is very promising.
Analytical Solution For Determination The Control Parameter In The Inverse Parabolic Equation Using Ham, M. M. Khader
Analytical Solution For Determination The Control Parameter In The Inverse Parabolic Equation Using Ham, M. M. Khader
Applications and Applied Mathematics: An International Journal (AAM)
In this article, the homotopy analysis method (HAM) for obtaining the analytical solution of the inverse parabolic problem and computing the unknown time-dependent parameter is introduced. The series solution is developed and the recurrence relations are given explicitly. Special attention is given to satisfy the convergence of the proposed method. A comparison of HAM with the variational iteration method is made. In the HAM, we use the auxiliary parameter ~ to control with a simple way in the convergence region of the solution series. Applying this method with several
Frechet Differentiable Norm And Locally Uniformly Rotund Renormings, Gaj R. Damai, Prakash M. Bajracharya
Frechet Differentiable Norm And Locally Uniformly Rotund Renormings, Gaj R. Damai, Prakash M. Bajracharya
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we study briefly the role played by the locally uniformly rotund (LUR) norm and Frechet differentiability of a norm on the Banach space theory. Our old outstanding open Problem 3.8 mentioned below is the main object of this paper. We study nearly about it and find some additional assumptions on the space attached with this problem to obtain its positive or negative answer. We investigate different results related to these norms and their duals on different settings. In particular, we introduce reflexive spaces, Banach spaces with unconditional basis, weakly locally uniformly rotund (WLUR) norm, Almost locally uniformly …
Asymptotic Behavior Of Waves In A Nonuniform Medium, Nezam Iraniparast, Lan Nguyen, Mikhail Khenner
Asymptotic Behavior Of Waves In A Nonuniform Medium, Nezam Iraniparast, Lan Nguyen, Mikhail Khenner
Applications and Applied Mathematics: An International Journal (AAM)
An incoming wave on an infinite string, that has uniform density except for one or two jump discontinuities, splits into transmitted and reflected waves. These waves can explicitly be described in terms of the incoming wave with changes in the amplitude and speed. But when a string or membrane has continuous inhomogeneity in a finite region the waves can only be approximated or described asymptotically. Here, we study the cases of monochromatic waves along a nonuniform density string and plane waves along a membrane with nonuniform density. In both cases the speed of the physical system is assumed to tend …
Thermal Stress Analysis In A Functionally Graded Hollow Elliptic-Cylinder Subjected To Uniform Temperature Distribution, V. R. Manthena, N. K. Lamba, G. D. Kedar
Thermal Stress Analysis In A Functionally Graded Hollow Elliptic-Cylinder Subjected To Uniform Temperature Distribution, V. R. Manthena, N. K. Lamba, G. D. Kedar
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, an analytical method of a thermoelastic problem for a medium with functionally graded material properties is developed in a theoretical manner for the elliptic-cylindrical coordinate system under the assumption that the material properties except for Poisson’s ratio and density are assumed to vary arbitrarily with the exponential law in the radial direction. An attempt has been made to reconsider the fundamental system of equations for functionally graded solids in a two-dimensional state under thermal and mechanical loads. The general solution of displacement formulation is obtained by the introduction of appropriate transformation and carried out the analysis by …
Inverse Problem For A Parabolic System, Reza Pourgholi, Amin Esfahani, Hassan D. Mazraeh
Inverse Problem For A Parabolic System, Reza Pourgholi, Amin Esfahani, Hassan D. Mazraeh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper a numerical approach combining the least squares method and a genetic algorithm is proposed for the determination of the source term in an inverse parabolic system (IPS). A numerical experiment confirm the utility of this algorithm as the results are in good agreement with the exact data. Results show that a reasonable estimation can be obtained by the genetic algorithm within a CPU with clock speed 2.7 GHz.
Numerical Simulation Of The Phase Space Of Jupiter-Europa System Including The Effect Of Oblateness, Vinay Kumar, Beena R. Gupta, Rajiv Aggarwal
Numerical Simulation Of The Phase Space Of Jupiter-Europa System Including The Effect Of Oblateness, Vinay Kumar, Beena R. Gupta, Rajiv Aggarwal
Applications and Applied Mathematics: An International Journal (AAM)
We have numerically investigated the phase space of the Jupiter-Europa system in the framework of a Circular Restricted Three-Body Problem. In our model, Jupiter is taken as oblate primary. We have considered time-frequency analysis (TFA) based on wavelets and the Poincare Surface of Section (PSS) for the characterization of orbits in the Jupiter-Europa model. We have exploited both cases: a system with and without considering the effect of oblateness. Graphs (ridge-plots) explaining the phenomenon of resonance trapping, a difference between chaotic sticky orbit and the non-sticky orbit, and periodic and quasi-periodic orbit are presented. Our results of Poincare surfaces of …
Damping In Microscale Modified Couple Stress Thermoelastic Circular Kirchhoff Plate Resonators, Rajneesh Kumar, Shaloo Devi, Veena Sharma
Damping In Microscale Modified Couple Stress Thermoelastic Circular Kirchhoff Plate Resonators, Rajneesh Kumar, Shaloo Devi, Veena Sharma
Applications and Applied Mathematics: An International Journal (AAM)
The vibrations of circular plate in modified couple stress thermoelastic medium using Kirchhoff- Love plate theory has been presented. The basic equations of motion and heat conduction equation for Lord Shulman (L-S, 1967) theory are written with the help of Kirchhoff-Love plate theory. The thermoelastic damping of micro beam resonators is studied by applying normal mode analysis method. The solutions for the free vibrations of plates under clamped, simply supported and free boundary conditions are obtained. The analytical expressions for thermoelastic damping of vibration and frequency shift are obtained for generalized couple stress thermoelastic and coupled thermoelastic plates. Numerical results …
Generalized Statistical Summability Of Double Sequences And Korovkin Type Approximation Theorem, M. Mursaleen
Generalized Statistical Summability Of Double Sequences And Korovkin Type Approximation Theorem, M. Mursaleen
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we introduce the notion of statistical (λ, μ)-summability and find its relation with (λ, μ)-statistical convergence. We apply this new method to prove a Korovkin type approximation theorem for functions of two variables. Furthermore, we provide an example in support to show that our result is stronger than the previous ones.
Effect Of Nonlinear Thermal Radiation On Mhd Chemically Reacting Maxwell Fluid Flow Past A Linearly Stretching Sheet, A. M. Ramireddy, J. V. Ramana Reddy, N. Sandeep, V. Sugunamma
Effect Of Nonlinear Thermal Radiation On Mhd Chemically Reacting Maxwell Fluid Flow Past A Linearly Stretching Sheet, A. M. Ramireddy, J. V. Ramana Reddy, N. Sandeep, V. Sugunamma
Applications and Applied Mathematics: An International Journal (AAM)
This communication addresses the influence of nonlinear thermal radiation on magneto hydrodynamic Maxwell fluid flow past a linearly stretching surface with heat and mass transfer. The effects of heat generation/absorption and chemical reaction are taken into account. At first, we converted the governing partial differential equations into nonlinear ordinary differential equations with the help of suitable similarity transformations and solved by using Runge-Kutta based shooting technique. Further, the effects of various physical parameters on velocity, temperature and concentration fields were discussed thoroughly with the help of graphs obtained by using bvp5c MATLAB package. In view of many engineering applications we …
Effect Of Damping And Thermal Gradient On Vibrations Of Orthotropic Rectangular Plate Of Variable Thickness, U. S. Rana, Robin Robin
Effect Of Damping And Thermal Gradient On Vibrations Of Orthotropic Rectangular Plate Of Variable Thickness, U. S. Rana, Robin Robin
Applications and Applied Mathematics: An International Journal (AAM)
In this present paper, damped vibrations of an orthotropic rectangular plate resting on elastic foundation with thermal gradient is modeled, considering variable thickness of plate. Following Le`vy approach, the governed equation of motion is solved numerically using quintic spline technique with clamped and simply supported edges. The effect of damping parameter and thermal gradient together with taper constant, density parameter and elastic foundation parameter on the natural frequencies of vibration for the first three modes of vibration are depicted through Tables and Figures, and mode shapes have been computed for fixed value of plate parameter. It has been observed that …
Some Relations On Generalized Rice's Matrix Polynomials, Ayman Shehata
Some Relations On Generalized Rice's Matrix Polynomials, Ayman Shehata
Applications and Applied Mathematics: An International Journal (AAM)
The main aim of this paper is to obtain certain properties of generalized Rice’s matrix polynomials such as their matrix differential equation, generating matrix functions, an expansion for them. We have also deduced the various families of bilinear and bilateral generating matrix functions for them with the help of the generating matrix functions developed in the paper and some of their applications have also been presented here.
New Structure For Exact Solutions Of Nonlinear Time Fractional Sharma-Tasso-Olver Equation Via Conformable Fractional Derivative, Hadi Rezazadeh, Farid S. Khodadad, Jalil Manafian
New Structure For Exact Solutions Of Nonlinear Time Fractional Sharma-Tasso-Olver Equation Via Conformable Fractional Derivative, Hadi Rezazadeh, Farid S. Khodadad, Jalil Manafian
Applications and Applied Mathematics: An International Journal (AAM)
In this paper new fractional derivative and direct algebraic method are used to construct exact solutions of the nonlinear time fractional Sharma-Tasso-Olver equation. As a result, three families of exact analytical solutions are obtained. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of nonlinear fractional partial differential equations.
Stability Of Triangular Libration Points In The Sun - Jupiter System Under Szebehely’S Criterion, M. R. Hassan, Md. A. Hassan, M. Z. Ali
Stability Of Triangular Libration Points In The Sun - Jupiter System Under Szebehely’S Criterion, M. R. Hassan, Md. A. Hassan, M. Z. Ali
Applications and Applied Mathematics: An International Journal (AAM)
In the present study, the classical fourth-order Runge-Kutta method with seventh-order automatic step-size control has been carried out to examine the stability of triangular libration points in the Sun-Jupiter system. The Sun is a highly luminous body and Jupiter is a highly spinning body, so radiation pressure of the Sun and oblateness of the Jupiter cannot be neglected. These factors must have some effects on the motion of the infinitesimal mass (spacecraft) and consequent effects on the stability of the triangular libration points. It is to be noted that in our problem, infinitesimal mass exerts no influence of attraction on …
Application Of Taylor-Pade Technique For Obtaining Approximate Solution For System Of Linear Fredholm Integro-Dierential Equations, M. M. Khader
Applications and Applied Mathematics: An International Journal (AAM)
In this article, we introduce a modification of the Taylor matrix method using Pad´e approximation to obtain an accurate solution of linear system of Fredholm integro-differential equations (FIDEs). This modification is based on, first, taking truncated Taylor series of the functions and then substituting their matrix forms into the given equations. Thereby the equation reduces to a matrix equation, which corresponds to a system of linear algebraic equations with unknown Taylor coefficients. Finally, we use Pad´e approximation to obtain an accurate numerical solution of the proposed problem. To demonstrate the validity and the applicability of the proposed method, we present …
Numerical Solution Of Fractional Elliptic Pde's By The Collocation Method, Fuat Usta
Numerical Solution Of Fractional Elliptic Pde's By The Collocation Method, Fuat Usta
Applications and Applied Mathematics: An International Journal (AAM)
In this presentation a numerical solution for the solution of fractional order of elliptic partial differential equation in R2 is proposed. In this method we use the Radial basis functions (RBFs) method to benefit the desired properties of mesh free techniques such as no need to generate any mesh and easily applied to multi dimensions. In the numerical solution approach the RBF collocation method is used to discrete fractional derivative terms with the Gaussian basis function. Two dimensional numerical examples are presented and discussed, which conform well with the corresponding exact solutions.
A Novel Approach For Solving Volterra Integral Equations Involving Local Fractional Operator, Hassan K. Jassim
A Novel Approach For Solving Volterra Integral Equations Involving Local Fractional Operator, Hassan K. Jassim
Applications and Applied Mathematics: An International Journal (AAM)
The paper presents an approximation method called local fractional variational iteration method (LFVIM) for solving the linear and nonlinear Volterra integral equations of the second kind with local fractional derivative operators. Some illustrative examples are discussed to demonstrate the efficiency and the accuracy of the proposed method. Furthermore, this method does not require spatial discretization or restrictive assumptions and therefore reduces the numerical computation significantly. The results reveal that the local fractional variational iteration method is very effective and convenient to solve linear and nonlinear integral equations within local fractional derivative operators.
Some Properties Of Certain Mixed Type Special Matrix Functions And Polynomials, Ahmed A. Al-Gonah, Fatima M. Al-Samadi
Some Properties Of Certain Mixed Type Special Matrix Functions And Polynomials, Ahmed A. Al-Gonah, Fatima M. Al-Samadi
Applications and Applied Mathematics: An International Journal (AAM)
By using certain operational methods, the authors introduce some new mixed type special matrix functions and polynomials. Some properties of these matrix functions and polynomials are established.
A Simple Linear Time Algorithm For Computing A 1-Median On Cactus Graphs, Kien T. Nguyen, Pham V. Chien, Ly H. Hai, Huynh D. Quoc
A Simple Linear Time Algorithm For Computing A 1-Median On Cactus Graphs, Kien T. Nguyen, Pham V. Chien, Ly H. Hai, Huynh D. Quoc
Applications and Applied Mathematics: An International Journal (AAM)
We address the problem of finding a 1-median on a cactus graph. The problem has already been solved in linear time by the algorithms of Burkard and Krarup (1998), and Lan and Wang (2000). These algorithms are complicated and need efforts. Hence, we develop in this paper a simpler algorithm. First, we construct a condition for a cycle that contains a 1-median or for a vertex that is indeed a 1-median of the cactus. Based on this condition, we localize the search for deriving a 1-median on the underlying cactus. Complexity analysis shows that the approach runs in linear time.
Numerical Solution Of Fractional Integro-Differential Equations With Nonlocal Conditions, M. Jani, D. Bhatta, S. Javadi
Numerical Solution Of Fractional Integro-Differential Equations With Nonlocal Conditions, M. Jani, D. Bhatta, S. Javadi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we present a numerical method for solving fractional integro-differential equations with nonlocal boundary conditions using Bernstein polynomials. Some theoretical considerations regarding fractional order derivatives of Bernstein polynomials are discussed. The error analysis is carried out and supported with some numerical examples. It is shown that the method is simple and accurate for the given problem.
Numerical Study Of Soliton Solutions Of Kdv, Boussinesq, And Kaup-Kuperschmidt Equations Based On Jacobi Polynomials, Khadijeh Sadri, Hamideh Ebrahimi
Numerical Study Of Soliton Solutions Of Kdv, Boussinesq, And Kaup-Kuperschmidt Equations Based On Jacobi Polynomials, Khadijeh Sadri, Hamideh Ebrahimi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a numerical method is developed to approximate the soliton solutions of some nonlinear wave equations in terms of the Jacobi polynomials. Wave are very important phenomena in dispersion, dissipation, diffusion, reaction, and convection. Using the wave variable converts these nonlinear equations to the nonlinear ODE equations. Then, the operational Collocation method based on Jacobi polynomials as bases is applied to approximate the solution of ODE equation resulted. In addition, the intervals of the solution will be extended using an rational exponential approximation (REA). The KdV, Boussinesq, and Kaup–Kuperschmidt equations are studied as the test examples. Finally, numerical …
Finite Difference Schemes For Variable Order Time-Fractional First Initial Boundary Value Problems, Gunvant A. Birajdar, M. M. Rashidi
Finite Difference Schemes For Variable Order Time-Fractional First Initial Boundary Value Problems, Gunvant A. Birajdar, M. M. Rashidi
Applications and Applied Mathematics: An International Journal (AAM)
The aim of the study is to obtain the numerical solution of first initial boundary value problem (IBVP) for semi-linear variable order fractional diffusion equation by using different finite difference schemes. We developed the three finite difference schemes namely explicit difference scheme, implicit difference scheme and Crank-Nicolson difference scheme, respectively for variable order type semi-linear diffusion equation. For this scheme the stability as well as convergence are studied via Fourier method. At the end, solution of some numerical examples are discussed and represented graphically using Matlab.
Application Of Kudryashov Method For The Ito Equations, Mozhgan Akbari
Application Of Kudryashov Method For The Ito Equations, Mozhgan Akbari
Applications and Applied Mathematics: An International Journal (AAM)
In this present work, the Kudryashov method is used to construct exact solutions of the (1+1)- dimensional and the (1+2)-dimensional form of the generalized Ito integro-differential equation. The Kudryashov method is a powerful method for obtaining exact solutions of nonlinear evolution equations. This method can be applied to non-integrable equations as well as integrable ones.
On The Convergence Of Two-Dimensional Fuzzy Volterra-Fredholm Integral Equations By Using Picard Method, Ali Ebadian, Foroozan Farahrooz, Amirahmad Khajehnasiri
On The Convergence Of Two-Dimensional Fuzzy Volterra-Fredholm Integral Equations By Using Picard Method, Ali Ebadian, Foroozan Farahrooz, Amirahmad Khajehnasiri
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we prove convergence of the method of successive approximations used to approximate the solution of nonlinear two-dimensional Volterra-Fredholm integral equations and define the notion of numerical stability of the algorithm with respect to the choice of the first iteration. Also we present an iterative procedure to solve such equations. Finally, the method is illustrated by solving some examples.
A Numerical Scheme For Generalized Fractional Optimal Control Problems, N. Singha, C. Nahak
A Numerical Scheme For Generalized Fractional Optimal Control Problems, N. Singha, C. Nahak
Applications and Applied Mathematics: An International Journal (AAM)
This paper introduces a generalization of the Fractional Optimal Control Problem (GFOCP). Proposed generalizations differ in terms of explaining the constraint involved in the dynamical system of the control problem. We assume the constraint as an arbitrary function of fractional derivatives and fractional integrals. By this assumption the restriction on constraint, to be of some prescribed function of fractional operators, is removed. Deduction of necessary optimality conditions followed by particular cases and examples has been provided. Additionally, we construct a solution scheme for the suggested class of (GFOCP)’s. The formulation of this scheme is done by implementing the Adomian decomposition …
On The Slow Growth And Approximation Of Entire Function Solutions Of Second-Order Elliptic Partial Differential Equations On Caratheodory Domains, Devendra Kumar
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we consider the regular, real-valued solutions of the second-order elliptic partial differential equation. The characterization of generalized growth parameters for entire function solutions for slow growth in terms of approximation errors on more generalized domains, i.e., Caratheodory domains, has been obtained. Moreover, we studied some inequalities concerning the growth parameters of entire function solutions of above equation for slow growth which have not been studied so far.
Heat Source Thermoelastic Problem In A Hollow Elliptic Cylinder Under Time-Reversal Principle, Pravin Bhad, Vinod Varghese, Lalsingh Khalsa
Heat Source Thermoelastic Problem In A Hollow Elliptic Cylinder Under Time-Reversal Principle, Pravin Bhad, Vinod Varghese, Lalsingh Khalsa
Applications and Applied Mathematics: An International Journal (AAM)
The article investigates the time-reversal thermoelasticity of a hollow elliptical cylinder for determining the temperature distribution and its associated thermal stresses at a certain point using integral transform techniques by unifying classical orthogonal polynomials as the kernel. Furthermore, by considering a circle as a special kind of ellipse, it is seen that the temperature distribution and the comparative study of a circular cylinder can be derived as a special case from the present mathematical solution. The numerical results obtained are accurate enough for practical purposes.
Implementation Of The Matrix Differential Transform Method For Obtaining An Approximate Solution Of Some Nonlinear Matrix Evolution Equations, M. M. Khader, A. Borhanifar
Implementation Of The Matrix Differential Transform Method For Obtaining An Approximate Solution Of Some Nonlinear Matrix Evolution Equations, M. M. Khader, A. Borhanifar
Applications and Applied Mathematics: An International Journal (AAM)
This article introduces the matrix differential transform method (MDTM) to apply to matrix partial differential equations (MPDEs) and employs it for solving matrix Fisher equations, matrix Burgers equations and matrix KdV equations. We show how the MDTM applies to the linear part and nonlinear part of any MPDE and give various examples of MPDEs to illustrate the efficiency of the method. The results obtained are in excellent agreement with the exact solution and show that the proposed method is powerful, accurate, and easy.